Calculating bits required to store decimal number

Question

This is a homework question that I am stuck with.

Consider unsigned integer representation. How many bits will be required to store a decimal number

Answer 1

The formula for the number of binary bits required to store n integers (for example, 0 to n - 1) is:

log_e(n) / log_e(2)

and round up.

For example, for values -128 to 127 (signed byte) or 0 to 255 (unsigned byte), the number of integers is 256, so n is 256, giving 8 from the above formula.

For 0 to n, use n + 1 in the above formula (there are n + 1 integers).

On your calculator, log_e may just be labelled log or ln (natural logarithm).